Biological order emerges from interactions between vast numbers of macromolecules at the cellular level, between hundreds of cells at the tissue and whole organism level, and between hundreds to thousands of individuals at the population level. Very little quantitative information is available that allows us to describe these interactions with sufficient realism to predict useful kinds of experiments that would have a decisive impact on our understanding of these very different levels of complexity. This is because the information for a serious analysis of many complex systems is only now becoming available, and because the analytical tools are either lacking or underdeveloped. Understanding is further complicated by the fact that the majority of biological systems are non-linear, and thus the outcome of many interacting systems is most often counterintuitive. Here we propose to study the emergence of form in a simple eukaryotic model organism, the cellular slime mold Dictyostelium. This organism, widely used to study the cytoskeleton, cell signaling, and morphogenesis, forms a distinctive and highly organized multicellular fruiting body which arises from a large population of randomly distributed free living amoebae. It is thus a prototypical example of how a complex dynamical system can arise from an initially random state. Our approach relies on detailed realistic quantitative modeling of chemotactic signaling between free living cells on their way to forming a mature differentiated tissue. This approach is combined with molecular and classical genetic analysis of predictions arising from the model. The goal is a detailed test of published models for the propagation of chemotactic waves and the establishment of oscillators in a field of excitable cells. These experiments will allow a deeper understanding of how waveforms, propagation velocities, and wave amplitude are chosen during early morphogenesis. The results will also have a direct bearing on our understanding of how waves propagate in other excitable systems, such as electrical waves in the beating heart, and Ca2+ waves which organize embryonic axes in many vertebrate eggs.